LONDON — Given red-carpet treatment in London, Chancellor Angela Merkel of Germany responded Thursday with warm words but few hard promises to Prime Minister David Cameron, who is counting on her support in his efforts to loosen British ties to the European Union.

Ms. Merkel became the first German chancellor to address both houses of Parliament since 1970, lunched at 10 Downing Street, then took afternoon tea with Queen Elizabeth II — an itinerary that underlined the importance Mr. Cameron attaches to the leader of the biggest European Union nation. By contrast the French president, François Hollande, was received recently at a military air base then taken to a country pub by Mr. Cameron for lunch.

In return for her top-notch treatment, Ms. Merkel offered warm praise for Britain’s historical contribution to Europe, and she joined cause with Mr. Cameron in calling for curbs on welfare entitlements for migrants crossing European Union frontiers. There should be freedom of movement for workers but not migration “into social security systems,” she told a news conference.

Yet, while keeping open the prospect of reforms to the 28-nation European Union, she pointedly declined to support Mr. Cameron’s efforts to rewrite the bloc’s founding treaties, a process that he believes will help him reshape British relations with Brussels.

From the start of her speech in the ornate Royal Gallery of the British Parliament, Ms. Merkel lowered expectations of what she could deliver for her host. “Some expect my speech to pave the way for a fundamental reform of the European architecture which will satisfy all kinds of alleged or actual British wishes. I am afraid they are in for a disappointment,” she said, speaking in clear English before switching to her native tongue.

“We need a strong United Kingdom with a strong voice inside the European Union,” Ms. Merkel said. “If we have that we will be able to make the necessary changes for the benefit of all.”

Though Mr. Cameron and Ms. Merkel also discussed the crisis in Ukraine, Britain’s anguished debate about its role in Europe dominated the talks. In January 2013, Mr. Cameron promised that, if re-elected next year, he would renegotiate British ties and then put the outcome of that agreement to a referendum on whether to stay in the European Union or quit.

German policy makers want Britain to remain, seeing its free-market economics as a counterbalance to the more statist approach of countries like France. Mr. Cameron has also invested in his personal relationship with Ms. Merkel, a fellow conservative, because she shares some of his worries about the rise of populism in Europe and about the Continent’s economic competitiveness.

But analysts say there is a limit to what Germany will contemplate, particularly when it comes to giving Britain special rights to opt out of policy areas.

“Merkel is keen on keeping the U.K. in the E.U.,” said Tanja Börzel, professor of European Integration at Berlin’s Free University, “she also shares its interest in strengthening the Single European Market, the E.U.'s competitiveness as well as its role as a global actor more broadly speaking. However, she is neither willing nor able to negotiate selective opt-outs for the U.K.”

She added: “Granting the U.K. further opt-outs would seriously threaten prospects for strengthening European integration in areas that are key to Germany by fueling the appetite of other member states to ask for their own opt-outs.”

Mr. Cameron’s desire for a full-scale treaty change is driven by the knowledge that he could veto any new agreement, something that would give him leverage in negotiations. Yet many other European nations dislike the idea, knowing that a full new treaty agreement could force them to hold referendums that they might easily lose.

Ms. Merkel instead suggested that only small, more technical, changes were on her agenda, saying that she wanted to adapt the rule book for the euro — which Germany uses but Britain does not — “in a limited, targeted and speedy way.”

Analysts said that there was never much prospect of a movement on Thursday. Mr. Cameron has yet to state what specific changes he wants to see in any detail, leaving his objectives fuzzy. Ms. Merkel’s political style is famously pragmatic and she rarely shows her hand early in any negotiation — let alone before it has begun.

And, while in London, Ms. Merkel also called on the leader of the opposition, Ed Miliband, a recognition that Mr. Cameron faces a difficult election next year and may never get the chance to conduct his promised renegotiation and referendum.